lan=0.201135240154868
avu=0.339999991578983
bvu=2.43399788367516
cvu=28.9000000000000
avd=0.199352390396591
bvd=2.37398788464852
cvd=26.5700000000000
as=0.814398752414996
bs=3.12460000000000
ag=5.89520000000000
bg=9.39900000000000
etas=-0.05995685462815492
etag=2.62262578872360
a0=0.003649615269729163
a1=0.02500000000000000
b1=10.7000000000000

aunorm=(((((Gamma[1+bvu] Gamma[avu+s])/(Gamma[1+avu+bvu+s]))+((cvu Gamma[1+bvu] Gamma[1+avu+s])/(Gamma[2+avu+bvu+s]))))^(-1))/.s->0;
x=.;
xδU=0.928 aunorm (x^avu)(((1-x))^bvu)(1+cvu x);


adnorm=(((((Gamma[1+bvd] Gamma[avd+s])/(Gamma[1+avd+bvd+s]))+((cvd Gamma[1+bvd] Gamma[1+avd+s])/(Gamma[2+avd+bvd+s]))))^(-1))/.s->0;
xδD=-(0.342 adnorm)  (x^avd)(((1-x))^bvd)(1+cvd x);

xδsn=asnormal etas (x^as)(((1-x))^bs);

asnormal=(((((Gamma[1+bs] Gamma[as+s])/(Gamma[1+as+bs+s]))))^(-1))/.s->0;

agnormal=(((((Gamma[1+bg] Gamma[ag+s])/(Gamma[1+ag+bg+s]))))^(-1))/.s->0;
xδgn=agnormal etag (x^ag)(((1-x))^bg);  
xδgn=agnormal etag (x^ag)(((1-x))^bg);  
LogLinearPlot[xδU,{x,0.0001,1}]
LogLinearPlot[xδD,{x,0.0001,1}]
LogLinearPlot[xδsn,{x,0.0001,1}]
LogLinearPlot[xδgn,{x,0.0001,1},PlotRange->All]

Needs["ErrorBarLogPlots`"]
E143g1pQ2={{0.031,0.008432,0.004639034},{0.035,0.01638,0.003541751},{0.039,0.011037,0.003169575},{0.044,0.014696,0.003019375},{0.049,0.016366,0.002805009},{0.056,0.017472,0.002746285},{0.063,0.016821,0.002610512},{0.071,0.020732,0.002584439},{0.079,0.024095,0.00258295},{0.09,0.02313,0.002376068},{0.101,0.029492,0.002484272},{0.113,0.029832,0.002526757},{0.128,0.032384,0.002748277},{0.144,0.032976,0.002769895},{0.162,0.039204,0.002973925},{0.182,0.042224,0.003255715},{0.205,0.046125,0.003305526},{0.23,0.04646,0.003510798},{0.259,0.062419,0.00417625},{0.292,0.057524,0.004570523},{0.329,0.058891,0.005315158},{0.37,0.05957,0.005500445},{0.416,0.073632,0.006184285},{0.468,0.070668,0.00695732},{0.526,0.073114,0.009186195},{0.592,0.06216,0.011387347},{0.666,0.04662,0.016039404},{0.749,0.05992,0.018784824}};
xg1nE143Q2={{0.031`,0.002635`,0.011984016`},{0.035`,-0.01421`,0.008856107`},{0.039`,0.005967`,0.007987387`},{0.044`,-0.01826`,0.007556223`},{0.049`,-0.020237`,0.007130637`},{0.056`,-0.0126`,0.007022364`},{0.063`,-0.014427`,0.006833395`},{0.071`,-0.01278`,0.00680897`},{0.079`,-0.01896`,0.006770535`},{0.09`,0.00135`,0.006570616`},{0.101`,-0.012625`,0.006639166`},{0.113`,-0.015368`,0.006716612`},{0.128`,0.002816`,0.007173712`},{0.144`,0.007632`,0.007517021`},{0.162`,-0.01539`,0.007858252`},{0.182`,0.011102`,0.008521022`},{0.205`,-0.01763`,0.008494523`},{0.23`,-0.01081`,0.00931429`},{0.259`,-0.037296`,0.011064485`},{0.292`,0.002628`,0.012281369`},{0.329`,0.011844`,0.014150825`},{0.37`,0.01147`,0.015451654`},{0.416`,-0.027872`,0.017152119`},{0.468`,-0.008424`,0.019188`},{0.526`,0.008416`,0.025171175`},{0.592`,-0.010656`,0.030475065`},{0.666`,-0.00999`,0.044746081`},{0.749`,0.025466`,0.054927802`}};
xg1DE143Q2={{0.031`,0.005146`,0.005125135`},{0.035`,0.001015`,0.003760668`},{0.039`,0.007878`,0.003386494`},{0.044`,-0.001672`,0.003212301`},{0.049`,-0.001715`,0.003018973`},{0.056`,0.00224`,0.002976441`},{0.063`,0.001701`,0.002879452`},{0.071`,0.003763`,0.002871772`},{0.079`,0.003002`,0.0028713`},{0.09`,0.0108`,0.002737243`},{0.101`,0.007979`,0.002856711`},{0.113`,0.007232`,0.002845267`},{0.128`,0.016384`,0.00298819`},{0.144`,0.01872`,0.003078368`},{0.162`,0.011502`,0.003276247`},{0.182`,0.025662`,0.003533801`},{0.205`,0.01394`,0.003632609`},{0.23`,0.01633`,0.003855503`},{0.259`,0.012691`,0.004523241`},{0.292`,0.027448`,0.005099561`},{0.329`,0.0329`,0.005745738`},{0.37`,0.03293`,0.006461772`},{0.416`,0.023712`,0.006860848`},{0.468`,0.029952`,0.008173269`},{0.526`,0.038924`,0.010213073`},{0.592`,0.025456`,0.011899053`},{0.666`,0.017316`,0.016039404`},{0.749`,0.035952`,0.018784824`}};

Q0=4;
aunorm=(((((Gamma[1+bvu] Gamma[avu+s])/(Gamma[1+avu+bvu+s]))+((cvu Gamma[1+bvu] Gamma[1+avu+s])/(Gamma[2+avu+bvu+s]))))^(-1))/.s->0;
x=Exp[-v];
xδU=0.928 aunorm (x^avu)(((1-x))^bvu)(1+cvu x);
δUn=LaplaceTransform[xδU,v,s];

adnorm=(((((Gamma[1+bvd] Gamma[avd+s])/(Gamma[1+avd+bvd+s]))+((cvd Gamma[1+bvd] Gamma[1+avd+s])/(Gamma[2+avd+bvd+s]))))^(-1))/.s->0;
xδD=-(0.342 adnorm)  (x^avd)(((1-x))^bvd)(1+cvd x);
δDn=LaplaceTransform[xδD,v,s];

xδsn=asnormal etas (x^as)(((1-x))^bs);

asnormal=(((((Gamma[1+bs] Gamma[as+s])/(Gamma[1+as+bs+s]))))^(-1))/.s->0;
δsn=LaplaceTransform[xδsn,v,s];

agnormal=(((((Gamma[1+bg] Gamma[ag+s])/(Gamma[1+ag+bg+s]))))^(-1))/.s->0;
xδgn=agnormal etag (x^ag)(((1-x))^bg);  


δgn=LaplaceTransform[xδgn,v,s];



Λ=lan^2;
Q0=4;

β0=11-(2/3)f;
β1=102-(38/3)f;
"Q=Input["Q"]"; 
αQ=4π((1/(β0*(y-Log[Λ])))-((β1)/(((β0))^3))((Log[y-Log[Λ]])/(((y-Log[Λ]))^2)));
αQ0=4π((1/(β0*(y0-Log[Λ])))-((β1)/(((β0))^3))((Log[y0-Log[Λ]])/(((y0-Log[Λ]))^2)));

AlfasQ=αQ;
AlfasQ0=αQ0;
(*αQ=4π((1/(β0*(y-Log[Λ]))));
αQ0=4π((1/(β0*(y0-Log[Λ]))));*)
taQ=Integrate[1/(4π)AlfasQ,y]/.y->Log[Q];
taQ0=Integrate[1/(4π)AlfasQ0,y0]/.y0->Log[Q0];
ta=taQ-taQ0;
cf=(4/3);
ca=3;
 tf=f;
tr=f/2;


ta2n=(1/(β0^6))(-((2 β1^2)/(27 (Log[Q]-Log[Λ])^3))+(β0^2 β1)/(2 (Log[Q]-Log[Λ])^2)-β0^4/(Log[Q]-Log[Λ])+(β1 (-2 β1+9 β0^2 (Log[Q]-Log[Λ])) Log[Log[Q]-Log[Λ]])/(9 (Log[Q]-Log[Λ])^3)-(β1^2 Log[Log[Q]-Log[Λ]]^2)/(3 (Log[Q]-Log[Λ])^3))-(1/(β0^6))(-((2 β1^2)/(27 (Log[Q0]-Log[Λ])^3))+(β0^2 β1)/(2 (Log[Q0]-Log[Λ])^2)-β0^4/(Log[Q0]-Log[Λ])+(β1 (-2 β1+9 β0^2 (Log[Q0]-Log[Λ])) Log[Log[Q0]-Log[Λ]])/(9 (Log[Q0]-Log[Λ])^3)-(β1^2 Log[Log[Q0]-Log[Λ]]^2)/(3 (Log[Q0]-Log[Λ])^3));

"Lo Input Spliting Function";



δpqq0=4-8/3(1/(s+1)+1/(s+2)+2(EulerGamma+PolyGamma[0,s+1]));
δpqg0=(1/2) f (-(1/(1+s))+(2/(2+s)));
δpgq0=(4/3) ((2/(1+s))-(1/(2+s)));
δpgg0=3 ((11/6)-(f/9)+(3/(1+s))-(3/(2+s))+(1/(3+s))+(1/(4+s))+HarmonicNumber[s]-HarmonicNumber[4+s]);
"NLO Input Spliting Function";

"=======================================";
δpnsp1=(-((ca cf)/2)+cf^2) (2/(1+s)^3-2/(1+s)^2+4/(1+s)-π^2/(3 (1+s))-2/(2+s)^3-2/(2+s)^2+0.040000000000000036`/(2+s)+π^2/(3 (2+s))+4/(3+s)^3-4.696`/(3+s)-(2 π^2)/(3 (3+s))-4/(4+s)^3+9.972000000000001`/(4+s)+(2 π^2)/(3 (4+s))+4/(5+s)^3-10.952`/(5+s)-(2 π^2)/(3 (5+s))-4/(6+s)^3+10.092`/(6+s)+(2 π^2)/(3 (6+s))-12.616000000000003`/(7+s)+2.4400000000000004`/(8+s)-3.3280000000000003`/(9+s)+0.8559999999999999`/(10+s)-0.20800000000000018`/(11+s)+4.4`/(12+s)+1/(1+s)^3 (-8+(1+s) Log[16]+2 (1+s) PolyGamma[0,1+s/2]-2 (1+s) PolyGamma[0,(1+s)/2]-(1+s)^2 PolyGamma[1,1+s/2]+(1+s)^2 PolyGamma[1,(1+s)/2])-1/(2+s)^3 (16/(1+s)^2+(12 s)/(1+s)^2+(2+s) Log[16]-2 (2+s) PolyGamma[0,1+s/2]+2 (2+s) PolyGamma[0,(1+s)/2]+(2+s)^2 PolyGamma[1,1+s/2]-(2+s)^2 PolyGamma[1,(1+s)/2])-1/(3+s)^3 2 (164/((1+s)^2 (2+s)^2)+(284 s)/((1+s)^2 (2+s)^2)+(188 s^2)/((1+s)^2 (2+s)^2)+(60 s^3)/((1+s)^2 (2+s)^2)+(8 s^4)/((1+s)^2 (2+s)^2)-4 (3+s) Log[2]-2 (3+s) PolyGamma[0,1+s/2]+2 (3+s) PolyGamma[0,(1+s)/2]+(3+s)^2 PolyGamma[1,1+s/2]-(3+s)^2 PolyGamma[1,(1+s)/2])-1/(4+s)^3 2 (2176/((1+s)^2 (2+s)^2 (3+s)^2)+(4392 s)/((1+s)^2 (2+s)^2 (3+s)^2)+(3504 s^2)/((1+s)^2 (2+s)^2 (3+s)^2)+(1408 s^3)/((1+s)^2 (2+s)^2 (3+s)^2)+(288 s^4)/((1+s)^2 (2+s)^2 (3+s)^2)+(24 s^5)/((1+s)^2 (2+s)^2 (3+s)^2)+4 (4+s) Log[2]-2 (4+s) PolyGamma[0,1+s/2]+2 (4+s) PolyGamma[0,(1+s)/2]+(4+s)^2 PolyGamma[1,1+s/2]-(4+s)^2 PolyGamma[1,(1+s)/2])-1/(5+s)^3 2 (57328/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(146144 s)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(162160 s^2)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(103728 s^3)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(42144 s^4)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(11160 s^5)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(1880 s^6)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(184 s^7)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(8 s^8)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)-4 (5+s) Log[2]-2 (5+s) PolyGamma[0,1+s/2]+2 (5+s) PolyGamma[0,(1+s)/2]+(5+s)^2 PolyGamma[1,1+s/2]-(5+s)^2 PolyGamma[1,(1+s)/2])-1/(6+s)^2 2 (Log[16]-2 PolyGamma[0,4+s/2]+2 PolyGamma[0,(7+s)/2]+(6+s) PolyGamma[1,4+s/2]-(6+s) PolyGamma[1,(7+s)/2]))+cf tf (-(1/6)-(2 π^2)/9-2/(3 (1+s)^2)-2/(9 (1+s))-2/(3 (2+s)^2)+22/(9 (2+s))+4/3 Zeta[2,1+s])+cf^2 (3/8-π^2/2-1/(1+s)^3-5/(1+s)-1/(2+s)^3+2/(2+s)^2+5/(2+s)+(2 (EulerGamma+PolyGamma[0,2+s]-(1+s) PolyGamma[1,2+s]))/(1+s)^2+(2 (EulerGamma+PolyGamma[0,3+s]-(2+s) PolyGamma[1,3+s]))/(2+s)^2-4 ((EulerGamma+PolyGamma[0,1+s]) PolyGamma[1,1+s]-1/2 PolyGamma[2,1+s])+6 Zeta[3]+3 PolyGamma[1,1+s])+ca cf (17/24+(11 π^2)/18-1/(1+s)^3+5/(6 (1+s)^2)+53/(18 (1+s))+π^2/(6 (1+s))-1/(2+s)^3+5/(6 (2+s)^2)-187/(18 (2+s))+π^2/(6 (2+s))-3 Zeta[3]-11/3 PolyGamma[1,1+s]-PolyGamma[2,1+s]);

"=======================================";
δpnsm1=-(-((ca cf)/2)+cf^2) (2/(1+s)^3-2/(1+s)^2+4/(1+s)-π^2/(3 (1+s))-2/(2+s)^3-2/(2+s)^2+0.040000000000000036`/(2+s)+π^2/(3 (2+s))+4/(3+s)^3-4.696`/(3+s)-(2 π^2)/(3 (3+s))-4/(4+s)^3+9.972000000000001`/(4+s)+(2 π^2)/(3 (4+s))+4/(5+s)^3-10.952`/(5+s)-(2 π^2)/(3 (5+s))-4/(6+s)^3+10.092`/(6+s)+(2 π^2)/(3 (6+s))-12.616000000000003`/(7+s)+2.4400000000000004`/(8+s)-3.3280000000000003`/(9+s)+0.8559999999999999`/(10+s)-0.20800000000000018`/(11+s)+4.4`/(12+s)+1/(1+s)^3 (-8+(1+s) Log[16]+2 (1+s) PolyGamma[0,1+s/2]-2 (1+s) PolyGamma[0,(1+s)/2]-(1+s)^2 PolyGamma[1,1+s/2]+(1+s)^2 PolyGamma[1,(1+s)/2])-1/(2+s)^3 (16/(1+s)^2+(12 s)/(1+s)^2+(2+s) Log[16]-2 (2+s) PolyGamma[0,1+s/2]+2 (2+s) PolyGamma[0,(1+s)/2]+(2+s)^2 PolyGamma[1,1+s/2]-(2+s)^2 PolyGamma[1,(1+s)/2])-1/(3+s)^3 2 (164/((1+s)^2 (2+s)^2)+(284 s)/((1+s)^2 (2+s)^2)+(188 s^2)/((1+s)^2 (2+s)^2)+(60 s^3)/((1+s)^2 (2+s)^2)+(8 s^4)/((1+s)^2 (2+s)^2)-4 (3+s) Log[2]-2 (3+s) PolyGamma[0,1+s/2]+2 (3+s) PolyGamma[0,(1+s)/2]+(3+s)^2 PolyGamma[1,1+s/2]-(3+s)^2 PolyGamma[1,(1+s)/2])-1/(4+s)^3 2 (2176/((1+s)^2 (2+s)^2 (3+s)^2)+(4392 s)/((1+s)^2 (2+s)^2 (3+s)^2)+(3504 s^2)/((1+s)^2 (2+s)^2 (3+s)^2)+(1408 s^3)/((1+s)^2 (2+s)^2 (3+s)^2)+(288 s^4)/((1+s)^2 (2+s)^2 (3+s)^2)+(24 s^5)/((1+s)^2 (2+s)^2 (3+s)^2)+4 (4+s) Log[2]-2 (4+s) PolyGamma[0,1+s/2]+2 (4+s) PolyGamma[0,(1+s)/2]+(4+s)^2 PolyGamma[1,1+s/2]-(4+s)^2 PolyGamma[1,(1+s)/2])-1/(5+s)^3 2 (57328/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(146144 s)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(162160 s^2)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(103728 s^3)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(42144 s^4)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(11160 s^5)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(1880 s^6)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(184 s^7)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)+(8 s^8)/((1+s)^2 (2+s)^2 (3+s)^2 (4+s)^2)-4 (5+s) Log[2]-2 (5+s) PolyGamma[0,1+s/2]+2 (5+s) PolyGamma[0,(1+s)/2]+(5+s)^2 PolyGamma[1,1+s/2]-(5+s)^2 PolyGamma[1,(1+s)/2])-1/(6+s)^2 2 (Log[16]-2 PolyGamma[0,4+s/2]+2 PolyGamma[0,(7+s)/2]+(6+s) PolyGamma[1,4+s/2]-(6+s) PolyGamma[1,(7+s)/2]))+cf tf (-(1/6)-(2 π^2)/9-2/(3 (1+s)^2)-2/(9 (1+s))-2/(3 (2+s)^2)+22/(9 (2+s))+4/3 Zeta[2,1+s])+cf^2 (3/8-π^2/2-1/(1+s)^3-5/(1+s)-1/(2+s)^3+2/(2+s)^2+5/(2+s)+(2 (EulerGamma+PolyGamma[0,2+s]-(1+s) PolyGamma[1,2+s]))/(1+s)^2+(2 (EulerGamma+PolyGamma[0,3+s]-(2+s) PolyGamma[1,3+s]))/(2+s)^2-4 ((EulerGamma+PolyGamma[0,1+s]) PolyGamma[1,1+s]-1/2 PolyGamma[2,1+s])+6 Zeta[3]+3 PolyGamma[1,1+s])+ca cf (17/24+(11 π^2)/18-1/(1+s)^3+5/(6 (1+s)^2)+53/(18 (1+s))+π^2/(6 (1+s))-1/(2+s)^3+5/(6 (2+s)^2)-187/(18 (2+s))+π^2/(6 (2+s))-3 Zeta[3]-11/3 PolyGamma[1,1+s]-PolyGamma[2,1+s]);
"=======================================";
δppsqq1=2 cf (-(2/(((1+s))^3))+(1/(((1+s))^2))+(1/(1+s))-(2/(((2+s))^3))-(3/(((2+s))^2))-(1/(2+s))) tf;
"======================================="; 
δpqq1=δppsqq1+δpnsm1;
"=======================================";
δpqg1=(1/(2 f))(ca tf (-(4/(((1+s))^3))-(2/(((1+s))^2))+(24/(1+s))-((2 (π^2))/(3 (1+s)))+(8/(((2+s))^3))-(16/(((2+s))^2))-(22/(2+s))+((4 (π^2))/(3 (2+s)))-((0.6560000000000001`)/(3+s))-((3.9639999999999995`)/(4+s))+((10.228`)/(5+s))+((2.7439999999999998`)/(6+s))-((6.392`)/(7+s))+((4.4`)/(8+s))+((8 HarmonicNumber[1+s])/(1+s))-((8 HarmonicNumber[2+s])/(2+s))+1/(((1+s))^3)(-8+(1+s) Log[16]+2 (1+s) PolyGamma[0,1+(s/2)]-2 (1+s) PolyGamma[0,((1+s)/2)]-(((1+s))^2) PolyGamma[1,1+(s/2)]+(((1+s))^2) PolyGamma[1,((1+s)/2)])-1/(((2+s))^3)2 ((16/(((1+s))^2))+((12 s)/(((1+s))^2))+(2+s) Log[16]-2 (2+s) PolyGamma[0,1+(s/2)]+2 (2+s) PolyGamma[0,((1+s)/2)]+(((2+s))^2) PolyGamma[1,1+(s/2)]-(((2+s))^2) PolyGamma[1,((1+s)/2)])+((2 ((π^2)+6 ((HarmonicNumber[1+s])^2)-6 PolyGamma[1,2+s]))/(6+6 s))-((4 ((π^2)+6 ((HarmonicNumber[2+s])^2)-6 PolyGamma[1,3+s]))/(12+6 s)))+cf tf (-(2/(((1+s))^3))+(9/(((1+s))^2))-(22/(1+s))+((2 (π^2))/(3 (1+s)))+(4/(((2+s))^3))+(27/(2+s))-((4 (π^2))/(3 (2+s)))-((8 HarmonicNumber[1+s])/(1+s))+((8 HarmonicNumber[2+s])/(2+s))-((2 ((π^2)+6 ((HarmonicNumber[1+s])^2)-6 PolyGamma[1,2+s]))/(6+6 s))+((4 (EulerGamma+PolyGamma[0,2+s]-(1+s) PolyGamma[1,2+s]))/(((1+s))^2))+((4 ((π^2)+6 ((HarmonicNumber[2+s])^2)-6 PolyGamma[1,3+s]))/(12+6 s))-((8 (EulerGamma+PolyGamma[0,3+s]-(2+s) PolyGamma[1,3+s]))/(((2+s))^2))));
"=======================================";
δpgq1=cf tf (-(16/(9 (1+s)))-(4/(9 (2+s)))+((8 HarmonicNumber[1+s])/(3 (1+s)))-((4 HarmonicNumber[2+s])/(3 (2+s))))-(cf^2) ((2/(((1+s))^3))+(2/(((1+s))^2))-(9/(2 (1+s)))-(1/(((2+s))^3))-(1/(2 (((2+s))^2)))+((2 HarmonicNumber[1+s])/(1+s))-((HarmonicNumber[2+s])/(2+s))-(((π^2)+6 ((HarmonicNumber[1+s])^2)-6 PolyGamma[1,2+s])/(6+6 s)))+ca cf ((5/(((1+s))^3))-(4/(((1+s))^2))+(41/(9 (1+s)))-((π^2)/(6 (1+s)))-(5/(2 (((2+s))^3)))+(13/(((2+s))^2))+(35/(9 (2+s)))+((π^2)/(12 (2+s)))+((0.32800000000000007`)/(3+s))+((2.4739999999999998`)/(4+s))-((1.157`)/(5+s))-((1.129`)/(6+s))+((1.624`)/(7+s))-((0.55`)/(8+s))-((10 HarmonicNumber[1+s])/(3 (1+s)))-((HarmonicNumber[2+s])/(3 (2+s)))-(1/(2 (((1+s))^3)))(-8+(1+s) Log[16]+2 (1+s) PolyGamma[0,1+(s/2)]-2 (1+s) PolyGamma[0,((1+s)/2)]-(((1+s))^2) PolyGamma[1,1+(s/2)]+(((1+s))^2) PolyGamma[1,((1+s)/2)])+(1/(4 (((2+s))^3)))((16/(((1+s))^2))+((12 s)/(((1+s))^2))+(2+s) Log[16]-2 (2+s) PolyGamma[0,1+(s/2)]+2 (2+s) PolyGamma[0,((1+s)/2)]+(((2+s))^2) PolyGamma[1,1+(s/2)]-(((2+s))^2) PolyGamma[1,((1+s)/2)])+((2 ((π^2)+6 ((HarmonicNumber[1+s])^2)-6 PolyGamma[1,2+s]))/(6+6 s))-((4 (EulerGamma+PolyGamma[0,2+s]-(1+s) PolyGamma[1,2+s]))/(((1+s))^2))-(((π^2)+6 ((HarmonicNumber[2+s])^2)-6 PolyGamma[1,3+s])/(12+6 s))+((2 (EulerGamma+PolyGamma[0,3+s]-(2+s) PolyGamma[1,3+s]))/(((2+s))^2)));
"=======================================";
δpgg1=-cf (1+4/(1+s)^3-10/(1+s)^2+10/(1+s)+4/(2+s)^3+2/(2+s)^2-10/(2+s)) tf-ca (4/3-4/(3 (1+s)^2)+56/(9 (1+s))-4/(3 (2+s)^2)-76/(9 (2+s))) tf+ca^2 (12.545675333333332` +4/(1+s)^3+134/(9 (1+s))-(2 π^2)/(3 (1+s))-8/(2+s)^3-268/(9 (2+s))+(4 π^2)/(3 (2+s))-(67 (EulerGamma+PolyGamma[0,1+s]))/9+1/3 π^2 (EulerGamma+PolyGamma[0,1+s])-1/9 (-67+3 π^2) (EulerGamma+PolyGamma[0,1+s])-(8 (EulerGamma+PolyGamma[0,2+s]-(1+s) PolyGamma[1,2+s]))/(1+s)^2+(16 (EulerGamma+PolyGamma[0,3+s]-(2+s) PolyGamma[1,3+s]))/(2+s)^2-4 ((EulerGamma+PolyGamma[0,1+s]) PolyGamma[1,1+s]-1/2 PolyGamma[2,1+s])-PolyGamma[2,1+s]);


phif=δpqq0+a0 δpqq1;
phig=δpgg0+a0 δpgg1;
thetaf=δpqg0+a0 δpqg1;
thetag=δpgq0+a0 δpgq1;
t=ta;
g0=δgn;
f0=δUn+δDn+2 f δsn;



gluon=
(E^(1/2 t (-2 b1+phif+phig-Sqrt[(phif-phig)^2+4 thetaf thetag])) (b1 (b1^2 E^(b1 t) ((-1+E^(t Sqrt[(phif-phig)^2+4 thetaf thetag])) (g0 (phif-phig)-2 f0 thetag)-g0 Sqrt[(phif-phig)^2+4 thetaf thetag]-E^(t Sqrt[(phif-phig)^2+4 thetaf thetag]) g0 Sqrt[(phif-phig)^2+4 thetaf thetag])+a1 E^(t Sqrt[(phif-phig)^2+4 thetaf thetag]) thetag (g0 thetaf (phif+phig+Sqrt[(phif-phig)^2+4 thetaf thetag])+f0 (2 thetaf thetag+phif (phif-phig+√((phif-phig)^2+4 thetaf thetag))))+a1 thetag (g0 thetaf (-phif-phig+Sqrt[(phif-phig)^2+4 thetaf thetag])+f0 (-2 thetaf thetag+phif (-phif+phig+√((phif-phig)^2+4 thetaf thetag))))+E^(b1 t) (-f0 thetag ((2+a1) phif^2-(4+a1) phif phig+a1 phif Sqrt[(phif-phig)^2+4 thetaf thetag]+2 (phig^2+(4+a1) thetaf thetag))+g0 (phif^3-phig^3-(4+a1) phig thetaf thetag+phig^2 Sqrt[(phif-phig)^2+4 thetaf thetag]-(-4+a1) thetaf thetag Sqrt[(phif-phig)^2+4 thetaf thetag]+phif^2 (-3 phig+√((phif-phig)^2+4 thetaf thetag))+phif (3 phig^2-(-4+a1) thetaf thetag-2 phig √((phif-phig)^2+4 thetaf thetag))))+E^(t (b1+Sqrt[(phif-phig)^2+4 thetaf thetag])) (f0 thetag ((2+a1) phif^2+2 (phig^2+(4+a1) thetaf thetag)-phif ((4+a1) phig+a1 √((phif-phig)^2+4 thetaf thetag)))+g0 (-phif^3+phig^3+(4+a1) phig thetaf thetag+phig^2 Sqrt[(phif-phig)^2+4 thetaf thetag]-(-4+a1) thetaf thetag Sqrt[(phif-phig)^2+4 thetaf thetag]+phif^2 (3 phig+√((phif-phig)^2+4 thetaf thetag))+phif (-3 phig^2+(-4+a1) thetaf thetag-2 phig √((phif-phig)^2+4 thetaf thetag)))))+4 a1 E^(1/2 t (b1+Sqrt[(phif-phig)^2+4 thetaf thetag])) (Sqrt[(phif-phig)^2+4 thetaf thetag] (g0 (phif-phig)^2 phig-g0 (phif-3 phig) thetaf thetag-b1^2 (g0 phig+f0 thetag)+f0 thetag (-phif phig+phig^2+2 thetaf thetag)) Cosh[1/2 t Sqrt[(phif-phig)^2+4 thetaf thetag]] Sinh[(b1 t)/2]+(b1^2 (f0 phif+g0 thetaf) thetag Cosh[(b1 t)/2]+(b1^2-(phif-phig)^2-4 thetaf thetag) (g0 (phif-phig) phig-(f0 phig+g0 thetaf) thetag) Sinh[(b1 t)/2]) Sinh[1/2 t Sqrt[(phif-phig)^2+4 thetaf thetag]])))/(2 b1 Sqrt[(phif-phig)^2+4 thetaf thetag] (-b1^2+(phif-phig)^2+4 thetaf thetag));

gama=
(E^(1/2 t (-2 b1+phif+phig-Sqrt[(phif-phig)^2+4 thetaf thetag])) (b1 (b1^2 E^(b1 t) (-(-1+E^(t Sqrt[(phif-phig)^2+4 thetaf thetag])) (f0 (phif-phig)+2 g0 thetaf)-f0 Sqrt[(phif-phig)^2+4 thetaf thetag]-E^(t Sqrt[(phif-phig)^2+4 thetaf thetag]) f0 Sqrt[(phif-phig)^2+4 thetaf thetag])+a1 thetaf (f0 thetag (-phif-phig+Sqrt[(phif-phig)^2+4 thetaf thetag])+g0 (-2 thetaf thetag+phig (phif-phig+Sqrt[(phif-phig)^2+4 thetaf thetag])))+a1 E^(t Sqrt[(phif-phig)^2+4 thetaf thetag]) thetaf (f0 thetag (phif+phig+Sqrt[(phif-phig)^2+4 thetaf thetag])+g0 (2 thetaf thetag+phig (-phif+phig+Sqrt[(phif-phig)^2+4 thetaf thetag])))+E^(t (b1+Sqrt[(phif-phig)^2+4 thetaf thetag])) (g0 thetaf (2 phif^2-(4+a1) phif phig+(2+a1) phig^2+2 (4+a1) thetaf thetag-a1 phig Sqrt[(phif-phig)^2+4 thetaf thetag])+f0 (phif^3+phif^2 (-3 phig+Sqrt[(phif-phig)^2+4 thetaf thetag])+(phig^2-(-4+a1) thetaf thetag) (-phig+Sqrt[(phif-phig)^2+4 thetaf thetag])+phif (3 phig^2+(4+a1) thetaf thetag-2 phig Sqrt[(phif-phig)^2+4 thetaf thetag])))+E^(b1 t) (-g0 thetaf (2 phif^2-(4+a1) phif phig+(2+a1) phig^2+2 (4+a1) thetaf thetag+a1 phig Sqrt[(phif-phig)^2+4 thetaf thetag])+f0 (-phif^3+(phig^2-(-4+a1) thetaf thetag) (phig+Sqrt[(phif-phig)^2+4 thetaf thetag])+phif^2 (3 phig+Sqrt[(phif-phig)^2+4 thetaf thetag])-phif (3 phig^2+(4+a1) thetaf thetag+2 phig Sqrt[(phif-phig)^2+4 thetaf thetag]))))+4 a1 E^(1/2 t (b1+Sqrt[(phif-phig)^2+4 thetaf thetag])) (Sqrt[(phif-phig)^2+4 thetaf thetag] (-b1^2 (f0 phif+g0 thetaf)+phif (phif-phig) (f0 phif-f0 phig+g0 thetaf)+thetaf (3 f0 phif-f0 phig+2 g0 thetaf) thetag) Cosh[1/2 t Sqrt[(phif-phig)^2+4 thetaf thetag]] Sinh[(b1 t)/2]+(b1^2 thetaf (g0 phig+f0 thetag) Cosh[(b1 t)/2]-(b1^2-(phif-phig)^2-4 thetaf thetag) (phif (f0 phif-f0 phig+g0 thetaf)+f0 thetaf thetag) Sinh[(b1 t)/2]) Sinh[1/2 t Sqrt[(phif-phig)^2+4 thetaf thetag]])))/(2 b1 Sqrt[(phif-phig)^2+4 thetaf thetag] (-b1^2+(phif-phig)^2+4 thetaf thetag));

δmnsNLOp=Exp[   ta  (δpqq0+ta2n/ta δpnsp1)];
δuvn=δmnsNLOp δUn;


δdvn=δmnsNLOp δDn;
δqbar=(gama-δuvn-δdvn)/6;

δcq=-(4/3) (9/2+π^2/3)+8/(3 (1+s))+4/(3 (2+s))+(4 (EulerGamma+PolyGamma[0,s+2]))/(3 (1+s))+(4 (EulerGamma+PolyGamma[0,s+3]))/(3 (2+s))+4/3 PolyGamma[1,1+s]+4/3 PolyGamma[1,3+s];
g1ns = 1/6 (δuvn - δdvn)(1+taQ δcq/(4 Pi));
x =.
k =.
j =.

Momentg1NLOxG1pNS = g1ns /. s -> j + 1 /. Q -> 12 /. f -> 4;
Nmax = 9;
α = 3;
β = 0.5;
θ = 
  Sqrt[((  k! (2  k + α + β + 1) Gamma[
     k + α + β + 1])/(
   Gamma[k + α + 1] Gamma[k + β + 1]))  ] (-1)^k/k! (∂_({x,k}))((x^(β+k))(((1-x))^(α+k)));
ckj = Sqrt[(( 
   k! (2 k + α + β + 1) Gamma[
     k + α + β + 1])/(
   Gamma[k + α + 1] Gamma[k + β + 1]))  ] (-1)^k/k! 1/
   j! (Pochhammer[-k, j] Pochhammer[α + β + k + 1, 
      j] Pochhammer[β + j + 1, k - j]);

aαβ[k_] := (∑_(j=0)^k)ckj*Momentg1NLOxG1pNS;

xG1pxQNS[x_] = ((∑_(k=0)^Nmax)θ*aαβ[k]);
Parallelize[Table[{x, xG1pxQNS[x]}, {x, 0.001, 0.009, 0.00025}]];
Parallelize[Table[{x, xG1pxQNS[x]}, {x, 0.01, 0.09, 0.0025}]];
Parallelize[Table[{x, xG1pxQNS[x]}, {x, 0.1, 0.99, 0.025}]];
Join[%%%, %%, %];
ListLogLinearPlot[%]

δqbar/.s->0/.f->6/.Q->200
δqbar/.s->0/.f->5/.Q->20
δqbar/.s->0/.f->4/.Q->10
δqbar/.s->0/.f->3/.Q->1

δuvn/.s->0/.f->6/.Q->200
δuvn/.s->0/.f->5/.Q->20
δuvn/.s->0/.f->4/.Q->10
δuvn/.s->0/.f->3/.Q->1

δdvn/.s->0/.f->6/.Q->200
δdvn/.s->0/.f->5/.Q->20
δdvn/.s->0/.f->4/.Q->10
δdvn/.s->0/.f->3/.Q->1

gluon/.s->0/.f->6/.Q->200
gluon/.s->0/.f->5/.Q->20
gluon/.s->0/.f->4/.Q->10
gluon/.s->0/.f->3/.Q->1

αQs=4π((1/(β0*(y-Log[Λ])))-((β1)/(((β0))^3))((Log[y-Log[Λ]])/(((y-Log[Λ]))^2)))/.y->Log[Q];
δcq=-(4/3) (9/2+π^2/3)+8/(3 (1+s))+4/(3 (2+s))+(4 (EulerGamma+PolyGamma[0,s+2]))/(3 (1+s))+(4 (EulerGamma+PolyGamma[0,s+3]))/(3 (2+s))+4/3 PolyGamma[1,1+s]+4/3 PolyGamma[1,3+s];
δcg=(1/2) ((2/(1+s))-(2/(2+s))+(((PolyGamma[0,s+1]+EulerGamma))/(1+s))-((2 ((PolyGamma[0,s+2]+EulerGamma)))/(2+s)));

αQ1=4π((1/(β0*(y-Log[Λ])))-((β1)/(((β0))^3))((Log[y-Log[Λ]])/(((y-Log[Λ]))^2)))/.y->Log[Q];
δgnn=gluon;
momg1NLO=1/2((1+taQ δcq/(4 Pi))(((4/9))(δuvn+2 δqbar )+((1/9))(δdvn+2 δqbar )+((1/9))(2 δqbar ))+(1/3)((4/9)+(1/9)+(1/9))taQ 2 δcg/(4 Pi)δgnn  )/.y->Log[Q];
Print["First Moment For g_1^p"]
momg1NLO/.Q->4.00000001/.f->4/.s->0
momg1NLO/.Q->20/.f->4/.s->0
momg1NLO/.Q->100/.f->5/.s->0
momg1NLO/.Q->200/.f->6/.s->0
(*momg1NLO=(1/2)(((4/9))(1+((αQ1)/(2π))δcq )(δuvn+2 δqbar )+((1/9))(1+((αQ1)/(2π))δcq )(δdvn+2 δqbar )+((1/9))(1+((αQ1)/(2 π))δcq )(2 δqbar )+(1/3)((4/9)+(1/9)+(1/9))((αQ1)/(2π)) 2 δcg δgnn  );*)
Print["First Moment For g_1^n"]
momg1nouNLO=momg1NLO-1/6(δuvn-δdvn)(1+ taQ δcq/(2 Pi));
momg1nouNLO/.f->4/.Q->4.0000000001/.s->0
momg1nouNLO/.f->4/.Q->20/.s->0
momg1nouNLO/.f->5/.Q->100/.s->0
momg1nouNLO/.f->6/.Q->200/.s->0

Print["First Moment For g_1^d"]
momg1d=(momg1nouNLO+momg1NLO)/2(1-3/2 0.058);
momg1d/.f->4/.Q->4.00000001/.s->0
momg1d/.f->4/.Q->20/.s->0
momg1d/.f->5/.Q->100/.s->0
momg1d/.f->6/.Q->200/.s->0

x=.
Momentg1NLOxG1p=momg1NLO/.s->j+1/.η->-1/.Q->5/.f->4;
Nmax=9;
α=3;
β=0.5;
θ=(Sqrt[((  k!(2  k+α+β+1) Gamma[k+α+β+1])/(Gamma[k+α+1]Gamma[k+β+1]))  ])((((-1))^k)/(k!))(∂_({x,k}))((x^(β+k))(((1-x))^(α+k)));
ckj=(Sqrt[(( k! (2 k+α+β+1) Gamma[k+α+β+1])/(Gamma[k+α+1]Gamma[k+β+1]))  ])((((-1))^k)/(k!))(1/(j!))(Pochhammer[-k,j]Pochhammer[α+β+k+1,j]Pochhammer[β+j+1,k-j]);

aαβ[k_]:=(∑_(j=0)^k)ckj*Momentg1NLOxG1p;

xG1pxQ[x_]=((∑_(k=0)^Nmax)θ*aαβ[k]);

%/.x->0.01
Parallelize[ Table[{x,xG1pxQ[x]},{x,0.001,0.009,0.00025}]];
Parallelize[ Table[{x,xG1pxQ[x]},{x,0.01,0.09,0.0025}]];
Parallelize[ Table[{x,xG1pxQ[x]},{x,0.1,0.99,0.025}]];
Join[%%%,%%,%];
ff=ListLogLinearPlot[%,PlotRange->All,Joined->True];
ErrorListLogLinearPlot[E143g1pQ2];
Show[%,%%]
NIntegrate[xG1pxQ[x]/x,{x,0,1}]

G1y=xG1pxQ[x]/x^2/.x->y;
Table[{x,-xG1pxQ[x]+x NIntegrate[G1y,{y,x,1}]},{x,0.001,0.009,0.00025}];
Table[{x,-xG1pxQ[x]+x NIntegrate[G1y,{y,x,1}]},{x,0.01,0.09,0.0025}];
Table[{x,-xG1pxQ[x]+x NIntegrate[G1y,{y,x,1}]},{x,0.1,0.99,0.025}];
Join[%%%,%%,%]
ListLogLinearPlot[%,PlotRange->All,Joined->True]

Table[{x,xG1pxQ[x]},{x,0.001,0.009,0.00025}];
Table[{x,xG1pxQ[x]},{x,0.01,0.09,0.0025}];
Table[{x,xG1pxQ[x]},{x,0.1,0.99,0.025}];
Join[%%%,%%,%];

Momentg1NLOxG1pn=momg1nouNLO/.s->j+1/.η->-1/.Q->5/.f->4;
Nmax=9;
α=3;
β=0.5;
θ=(Sqrt[((  k!(2  k+α+β+1) Gamma[k+α+β+1])/(Gamma[k+α+1]Gamma[k+β+1]))  ])((((-1))^k)/(k!))(∂_({x,k}))((x^(β+k))(((1-x))^(α+k)));
ckj=(Sqrt[(( k! (2 k+α+β+1) Gamma[k+α+β+1])/(Gamma[k+α+1]Gamma[k+β+1]))  ])((((-1))^k)/(k!))(1/(j!))(Pochhammer[-k,j]Pochhammer[α+β+k+1,j]Pochhammer[β+j+1,k-j]);

aαβn[k_]:=(∑_(j=0)^k)ckj*Momentg1NLOxG1pn;

xG1pxQn[x_]=((∑_(k=0)^Nmax)θ*aαβn[k]);
Parallelize[ Table[{x,xG1pxQn[x]/x},{x,0.001,0.009,0.00025}]];
Parallelize[ Table[{x,xG1pxQn[x]/x},{x,0.01,0.09,0.0025}]];
Parallelize[ Table[{x,xG1pxQn[x]/x},{x,0.1,0.99,0.025}]];
Join[%%%,%%,%];
ListLogLinearPlot[%,PlotRange->All,Joined->True]

Parallelize[ Table[{x,xG1pxQn[x]},{x,0.001,0.009,0.00025}]];
Parallelize[ Table[{x,xG1pxQn[x]},{x,0.01,0.09,0.0025}]];
Parallelize[ Table[{x,xG1pxQn[x]},{x,0.1,0.99,0.025}]];
Join[%%%,%%,%];
ListLogLinearPlot[%,PlotRange->All,Joined->True];
ErrorListLogLinearPlot[xg1nE143Q2];
Show[%,%%]

Momentg1NLOxG1pd=momg1d/.s->j+1/.η->-1/.Q->2/.f->4;
Nmax=9;
α=3;
β=0.5;
θ=(Sqrt[((  k!(2  k+α+β+1) Gamma[k+α+β+1])/(Gamma[k+α+1]Gamma[k+β+1]))  ])((((-1))^k)/(k!))(∂_({x,k}))((x^(β+k))(((1-x))^(α+k)));
ckj=(Sqrt[(( k! (2 k+α+β+1) Gamma[k+α+β+1])/(Gamma[k+α+1]Gamma[k+β+1]))  ])((((-1))^k)/(k!))(1/(j!))(Pochhammer[-k,j]Pochhammer[α+β+k+1,j]Pochhammer[β+j+1,k-j]);

aαβd[k_]:=(∑_(j=0)^k)ckj*Momentg1NLOxG1pd;

xG1pxQd[x_]=((∑_(k=0)^Nmax)θ*aαβd[k]);
LogLinearPlot[{xG1pxQd[x]},{x,0.001,0.99},PlotRange->All];
ErrorListLogLinearPlot[xg1DE143Q2];
Show[%,%%]

x=.
g1=gluon/.Q->10/.f->4;
twoN=8;
prec=70;

NInverseLaplaceTransformBlock[g1,s,v,twoN,prec]:=Module[{Omega,Alpha,M,p,den,r,num},(M=2*Ceiling[twoN/2];p=PadeApproximant[Exp[z],{z,0,{M-1,M}}];
den=Denominator[p];r=Roots[den==0,z];Alpha=Table[r[[i,2]],{i,1,M}];
num=Numerator[p];hospital=num/D[den,z];
Omega=SetPrecision[Table[hospital/.z->Alpha[[i]],{i,1,M,2}],prec+50];
Alpha=SetPrecision[Table[Alpha[[i]],{i,1,M,2}],prec]);
SetPrecision[-(2/v)Sum[Re[Omega[[i]] g1/.s->Alpha[[i]]/v],{i,1,M/2}],30]]
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[g1,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.0001,0.0009,0.000025}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[g1,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.001,0.009,0.00025}]];
Parallelize[Table[{xx,Re[NInverseLaplaceTransformBlock[g1,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.01,0.09,0.0025}]];
Parallelize[Table[{xx,  Re[NInverseLaplaceTransformBlock[g1,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.1,0.99,0.025}]];
Join[%%%%,%%%,%%,%];
ListLogLinearPlot[%];
LogLinearPlot[xδgn,{x,0.0001,1},PlotRange->All];
Show[%,%%,PlotRange->All]

x=.
gamma=gama/.Q->10/.f->4/.η->-1;
twoN=8;
prec=70;

NInverseLaplaceTransformBlock[gamma,s,v,twoN,prec]:=Module[{Omega,Alpha,M,p,den,r,num},(M=2*Ceiling[twoN/2];p=PadeApproximant[Exp[z],{z,0,{M-1,M}}];
den=Denominator[p];r=Roots[den==0,z];Alpha=Table[r[[i,2]],{i,1,M}];
num=Numerator[p];hospital=num/D[den,z];
Omega=SetPrecision[Table[hospital/.z->Alpha[[i]],{i,1,M,2}],prec+50];
Alpha=SetPrecision[Table[Alpha[[i]],{i,1,M,2}],prec]);
SetPrecision[-(2/v)Sum[Re[Omega[[i]] gamma/.s->Alpha[[i]]/v],{i,1,M/2}],30]]
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[gamma,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.001,0.009,0.00025}]];
Parallelize[Table[{xx,Re[NInverseLaplaceTransformBlock[gamma,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.01,0.09,0.0025}]];
Parallelize[Table[{xx,  Re[NInverseLaplaceTransformBlock[gamma,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.1,0.9,0.025}]];
Join[%%%,%%,%];
ListLogLinearPlot[%];
LogLinearPlot[xδU+xδD+6 xδsn,{x,0.001,1}];
Show[%,%%,PlotRange->All]

qbar=δqbar/.Q->10/.f->4;
twoN=8;
prec=70;

NInverseLaplaceTransformBlock[qbar,s,v,twoN,prec]:=Module[{Omega,Alpha,M,p,den,r,num},(M=2*Ceiling[twoN/2];p=PadeApproximant[Exp[z],{z,0,{M-1,M}}];
den=Denominator[p];r=Roots[den==0,z];Alpha=Table[r[[i,2]],{i,1,M}];
num=Numerator[p];hospital=num/D[den,z];
Omega=SetPrecision[Table[hospital/.z->Alpha[[i]],{i,1,M,2}],prec+50];
Alpha=SetPrecision[Table[Alpha[[i]],{i,1,M,2}],prec]);
SetPrecision[-(2/v)Sum[Re[Omega[[i]] qbar/.s->Alpha[[i]]/v],{i,1,M/2}],30]]
NIntegrate[ Re[NInverseLaplaceTransformBlock[qbar,s,v,twoN,prec]]/.v->Log[1/xx],{xx,0,1}]
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[qbar,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.0001,0.0009,0.000025}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[qbar,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.001,0.009,0.00025}]];
Parallelize[Table[{xx,Re[NInverseLaplaceTransformBlock[qbar,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.01,0.09,0.0025}]];
Parallelize[Table[{xx,  Re[NInverseLaplaceTransformBlock[qbar,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.1,0.99,0.025}]];
Join[%%%%,%%%,%%,%];
ListLogLinearPlot[%];
LogLinearPlot[xδsn,{x,0.0001,1}];
Show[%,%%,PlotRange->All]

uva=δuvn/.Q->10/.f->4;
twoN=8;
prec=70;

NInverseLaplaceTransformBlock[  uva,s,v,twoN,prec]:=Module[{Omega,Alpha,M,p,den,r,num},(M=2*Ceiling[twoN/2];p=PadeApproximant[Exp[z],{z,0,{M-1,M}}];
den=Denominator[p];r=Roots[den==0,z];Alpha=Table[r[[i,2]],{i,1,M}];
num=Numerator[p];hospital=num/D[den,z];
Omega=SetPrecision[Table[hospital/.z->Alpha[[i]],{i,1,M,2}],prec+50];
Alpha=SetPrecision[Table[Alpha[[i]],{i,1,M,2}],prec]);
SetPrecision[-(2/v)Sum[Re[Omega[[i]] uva /.s->Alpha[[i]]/v],{i,1,M/2}],30]]
NIntegrate[Re[NInverseLaplaceTransformBlock[uva,s,v,twoN,prec]]/.v->Log[1/xx],{xx,0,1}]

uva=δuvn/.Q->10/.f->4;
twoN=8;
prec=70;

NInverseLaplaceTransformBlock[uva,s,v,twoN,prec]:=Module[{Omega,Alpha,M,p,den,r,num},(M=2*Ceiling[twoN/2];p=PadeApproximant[Exp[z],{z,0,{M-1,M}}];
den=Denominator[p];r=Roots[den==0,z];Alpha=Table[r[[i,2]],{i,1,M}];
num=Numerator[p];hospital=num/D[den,z];
Omega=SetPrecision[Table[hospital/.z->Alpha[[i]],{i,1,M,2}],prec+50];
Alpha=SetPrecision[Table[Alpha[[i]],{i,1,M,2}],prec]);
SetPrecision[-(2/v)Sum[Re[Omega[[i]] uva/.s->Alpha[[i]]/v],{i,1,M/2}],30]]
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[uva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.0001,0.0009,0.000025}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[uva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.001,0.009,0.00025}]];
Parallelize[Table[{xx,Re[NInverseLaplaceTransformBlock[uva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.01,0.09,0.0025}]];
Parallelize[Table[{xx,  Re[NInverseLaplaceTransformBlock[uva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.1,0.99,0.025}]];
Join[%%%%,%%%,%%,%];
ListLogLinearPlot[%];
LogLinearPlot[xδU,{x,0.0001,1}];
Show[%,%%]

dva=δdvn/.Q->10/.f->4;
twoN=8;
prec=70;

NInverseLaplaceTransformBlock[dva,s,v,twoN,prec]:=Module[{Omega,Alpha,M,p,den,r,num},(M=2*Ceiling[twoN/2];p=PadeApproximant[Exp[z],{z,0,{M-1,M}}];
den=Denominator[p];r=Roots[den==0,z];Alpha=Table[r[[i,2]],{i,1,M}];
num=Numerator[p];hospital=num/D[den,z];
Omega=SetPrecision[Table[hospital/.z->Alpha[[i]],{i,1,M,2}],prec+50];
Alpha=SetPrecision[Table[Alpha[[i]],{i,1,M,2}],prec]);
SetPrecision[-(2/v)Sum[Re[Omega[[i]] dva/.s->Alpha[[i]]/v],{i,1,M/2}],30]]
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[dva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.0001,0.0009,0.000025}]];
Parallelize[Table[{xx, Re[NInverseLaplaceTransformBlock[dva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.001,0.009,0.00025}]];
Parallelize[Table[{xx,Re[NInverseLaplaceTransformBlock[dva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.01,0.09,0.0025}]];
Parallelize[Table[{xx,  Re[NInverseLaplaceTransformBlock[dva,s,v,twoN,prec]]/.v->Log[1/xx]},{xx,0.1,0.99,0.025}]];
Join[%%%%,%%%,%%,%];
ListLogLinearPlot[%];
LogLinearPlot[xδD,{x,0.0001,1}];
Show[%,%%]